Definitions:
Field mill: A device in which a conductor is alternately exposed to the electric-field to be measured and then shielded from it. Syn: Generating voltmeter, generating electric-field meter.
Vibrating plate electric-field meter: A device in which a sensing plate is modulated below the aperture of a faceplate in the electric-field to be measured. Syn: Vibrating probe.
Measurements of DC Electric-Fields
Three types of DC electric-field sensors have been used in science and engineering: shutter-type, vibrating plate, and cylindrical field mills. These devices determine the electric-field by measuring modulated, capacitively induced charges or currents sensed by conducting electrodes. Other instrumentation capable of measuring DC electric-fields exists (for example, radiation probes), but they are very specialized and do not find a wide-range of applications.
The shutter-type electric-field mill is the instrument mostly widely discussed in the literature (See FIG. 1). Indeed, many versions of this instrument are covered by patents. Harnwell and Van Voorhis (1933) were the first to propose this type of sensor. Field mills have a sensing electrode that is periodically exposed and shielded from the electric-field by a grounded rotating shutter. Shutter-type field mills are grounded and distort the electric-fields in their vicinity. The charge qs induced by ambient electric fields in its sensing electrode at any time instant t, as well as the induced current is, between the ground and the electrode is alternately exposed and shielded as it moves. The charge and the current are proportional to the amplitude of the component of the local electric-field (E) perpendicular to the shutter surface. The signal of the charge, and therefore the direction of the current, depends on the polarity of the field. Shutter type field mills distort the electric-field and are not capable of measuring the electric-field vector or the field gradient. Thus, they must be calibrated in the same situation (geometry, surrounding materials, charge distribution, etc) that will be encountered during measurements. Thus, the calibration procedure can be complex and vary with time in the dynamical situations frequently encountered in industrial processes.
Shutter-type field mills usually measure the magnitude of the electric-field by measuring the current between the ground and the sensing electrode:
                                                        i              s                        ⁡                          (              t              )                                =                                                    ⅆ                                                      q                    s                                    ⁡                                      (                    t                    )                                                                              ⅆ                t                                      =                                          ɛ                0                            ⁢              E              ⁢                                                ⅆ                                      a                    ⁡                                          (                      t                      )                                                                                        ⅆ                  t                                                                    ,                            (        1        )            
where ε0 is the permittivity of free space, qs(t) and a(t) are the induced charge and exposed area of the sensing element at time t (FIG. 1). This type of mill has a frequency response less than ½ the commutation rate, which is the rotation rate times the number of vanes. A typical frequency response is DC to 10 Hz or less. The shape of a(t) is generally triangular but this is not critical because the current is(t) is sampled once per commutation at its peak value.
A specific type of quadrature modulation has been applied to the shutter-type field mill, U.S. Pat. No. 6,608,483, which improves the range of the frequency response. In this case, the shape of a(t) is important because of the type of signal processing used, with the triangular waveform being the ideal. The treatment of DC fields is straightforward, and the commutation rate no longer limits the upper frequency response. However, the triangular waveform produces errors in the transient response. The errors depend on the timing of transient with respect to the shutter angular position. These time domain errors also produce errors in the frequency response. In addition, these shutter type field mills are subject to noise caused by the sliding brush contact with the rotating grounded shutter.
DC electric fields can also be measured with vibrating plate sensors (Comber et al., 1983). However, this type of sensor is not widely used because it is less sensitive than field mills. Like the shutter-type field mills, vibrating plate field meters are grounded and distort the electric field in their vicinity. Moreover, they only measure the amplitude of the component of the electric field perpendicular to its sensing plate. Therefore, vibrating plate field meters also require complex calibrations and are not suitable for typical industrial applications.
A less common type of field mill described in the literature is the cylindrical field mill (See FIG. 2). Kirkpatrick and Miyake (1932) were the first to discuss this type of sensor. Grounded cylindrical fields mills have been developed further by Maruvada et al. (1983), while a new class of isolated cylindrical field mills was developed by Kirkham et al. (1987) and Johnston and Kirkham (1989). Except for small effects due to the charging of the sensor and its image on nearby objects, isolated field mills do not distort the electric-field in their vicinity. Usually, cylindrical field mills measure the electric field by measuring the amplitude and phase of the current ic(t) flowing between two half-cylinder electrodes rotating with constant angular velocity ω, and connected to each other by a low-impedance measuring circuit (FIG. 2). Thus, in cylindrical field mills:ic(t)=4ε0rLEω sin(ωt+φ),   (2)
where r is the radius and L the length of each electrode, and φ is the phase of the two-dimensional electric field perpendicular to the axis of rotation with respect to a reference.
Cylindrical field mills also measure ion currents along the space field lines terminating on them. This poses a problem for grounded field mills because they cannot distinguish the currents due to the ion fluxes from that due to the local electric field. However, this effect can be removed by the use of two cylinders rotating at different angular velocities ω. This is not a problem in isolated field mills because their electrodes are quickly charged in the presence of ion currents and prevents further ion flow into the electrodes. With two orthogonally mounted sensors, it is possible to measure the 3-dimensional electric field, and a single sensor can measure the 2-dimensional field perpendicular to its axis of rotation.
In the prior art, cylindrical field mills have a pair of isolated conducting surfaces connected by a current measuring circuit as shown in FIG. 2. There are significant differences between this device and the shutter type field mill. The cylindrical mill has no grounded shutter, and in fact can be operated either grounded or isolated from ground. Both devices have rotating components that produce a measurable AC signal based on the DC external or ambient electric field. Rather than a sensing surface that is alternately shielded and unshielded by grounded elements however, the cylindrical field mill contains a fixed volume enclosed by a conductive surface. A fixed volume covered by a conducting surface shorts the external or ambient electric field, and therefore experiences a redistribution of surface charge that cancels any internal electric field. The charge distribution is proportional to the ambient electric field. The current flow produced by the charge redistribution as the cylinder rotates can be measured as it passes through a low impedance measuring circuit, referred to as an inverting type circuit. The cylindrical field mill can also measure field vectors in two dimensions while the shutter type field mill cannot. Finally, an important difference between cylindrical field mills and shutter sensors is that the current induced by uniform ambient fields is sinusoidal on cylindrical field mills, but it is roughly triangular in the prior art of the shutter type mills. Thus, the quadrature measurement technique described below can accurately reproduce the characteristics of the electric field over the frequency range of interest in our cylindrical field mill device, but not in the shutter type field mills discussed previously. Indeed, the triangular form of quadrature modulation used in the prior art introduces errors in the measurements. This significant difference provides a distinct improvement in the current design over the prior art.
The present invention is aimed at one or more of the problems identified above.